Experimental set up

A compound channel setup was used for this case study. The paper including all information about the experience was found in Proust and Nikora (2020), data are available in PROUST and NIKORA (2025).

Main features for the estimation

Laboratory measurements

Take a look about all the measurements:

Experiment: 1_WSE_floodplain_realistic_uncertainty

Here the experiment with the observational data obtained in the laboratory,averaging the values of the WSE.

Calibration data

A sample was taken of all measurements shown previously:

Check MCMC

All MCMC samples:

MCMC cooked:

Corelation plot of MCMC cooked:

Check summary

Zoom into the MAP and standard deviation of the error model: WSE in mm, discharge in m3/s, velocity in m/s kmin and kmoy in m1/3/s.
a0_min a0_flood Y1_intercept Y2_intercept Y3_intercept Y4_intercept Y5_intercept
N 2001.0000000 2001.000000 2.00100e+03 2001.000000 2001.000000 2001.000000 2001.000000
Minimum 107.4760000 23.356700 1.50000e-06 5.350170 5.473510 7.743410 6.253130
Maximum 130.0730000 46.343400 1.75630e-03 17.402300 22.259300 30.763900 27.444300
Range 22.5970000 22.986700 1.75480e-03 12.052100 16.785800 23.020500 21.191200
Mean 120.2120000 32.501500 2.06800e-04 10.045000 10.231900 15.379100 15.357700
Median 119.6200000 32.874100 1.71700e-04 9.793080 10.025000 15.268400 15.098500
Q10% 114.0310000 26.350600 3.29000e-05 7.671800 7.533980 11.570400 11.315500
Q25% 116.5180000 28.121200 6.60000e-05 8.672890 8.635640 13.172900 12.937500
Q75% 124.5030000 36.109800 3.06300e-04 11.206600 11.669000 17.080600 17.506600
Q90% 126.5360000 38.714200 4.31000e-04 12.853100 13.112000 19.466900 19.593900
St.Dev. 4.8327100 4.779110 1.78100e-04 1.971020 2.200820 3.108970 3.275740
Variance 23.3551000 22.839900 0.00000e+00 3.884940 4.843600 9.665710 10.730500
CV 0.0402015 0.147042 8.61514e-01 0.196220 0.215094 0.202156 0.213297
Skewness 0.0730142 0.104323 2.22869e+00 0.635261 0.571186 0.611240 0.543355
Kurtosis -0.9667830 -0.821106 1.15867e+01 0.351366 0.620198 1.211530 0.343737
MaxPost 119.8560000 32.305200 6.37000e-05 10.483900 9.980640 13.988500 15.570500
a0_min a0_flood Y1_intercept Y2_intercept Y3_intercept Y4_intercept Y5_intercept
St.Dev. 4.83271 4.77911 0.1781380 1.97102 2.20082 3.10897 3.27574
MaxPost 119.85600 32.30520 0.0636728 10.48390 9.98064 13.98850 15.57050

Estimation of the friction coefficients

In the main channel:

Estimation of the friction coefficients

In the floodplain:

Residuals

in terms of WSE

In terms of discharge

Notes:

  • High negative corelation between a0_kmin and a0_kmoy. They can be interchangeable and the result will be the same with a weighting or factor to compensate.

Question 1:

How to reduce the corelation between a0_kmin and a0_kmoy using only a single event?

1st proposal: reduce the uncertainty in the observational data

Experiment: 1_WSE_floodplain_low_uncertainty

Calibration data

A sample was taken of all measurements shown previously:

Check MCMC

All MCMC samples:

MCMC cooked:

Corelation plot of MCMC cooked:

Check summary

Zoom into the MAP and standard deviation of the error model: WSE in mm, discharge in m3/s, velocity in m/s kmin and kmoy in m1/3/s.
a0_min a0_flood Y1_intercept Y2_intercept Y3_intercept Y4_intercept Y5_intercept
N 2001.0000000 2001.000000 2.00100e+03 2001.000000 2001.000000 2001.000000 2001.000000
Minimum 107.4770000 24.728800 2.28700e-04 5.858510 5.162780 7.256530 8.535670
Maximum 128.5200000 47.267600 1.02860e-03 19.895200 19.534400 26.391600 25.783100
Range 21.0430000 22.538800 7.99900e-04 14.036700 14.371600 19.135100 17.247400
Mean 117.0700000 35.709300 4.68000e-04 10.422800 10.340100 15.183500 15.256800
Median 116.6180000 35.924800 4.40500e-04 10.168100 10.021500 15.076100 14.853100
Q10% 111.3130000 29.928700 3.08800e-04 7.961250 7.902230 11.555500 11.659700
Q25% 114.0760000 31.904100 3.64800e-04 9.012630 8.877260 13.179400 13.159800
Q75% 120.6260000 38.717500 5.48300e-04 11.564200 11.582200 17.017600 17.146600
Q90% 122.3280000 42.365800 6.64100e-04 13.277000 13.104500 18.888700 19.327900
St.Dev. 4.3978600 4.729290 1.39500e-04 2.099750 2.128930 2.922280 3.026050
Variance 19.3412000 22.366200 0.00000e+00 4.408930 4.532330 8.539750 9.156990
CV 0.0375661 0.132438 2.98147e-01 0.201457 0.205891 0.192464 0.198341
Skewness 0.1696110 0.105879 8.07301e-01 0.714238 0.737369 0.450935 0.561829
Kurtosis -0.6100620 -0.633168 4.67690e-01 0.821512 1.008740 0.474089 0.139611
MaxPost 118.9850000 33.238100 3.34500e-04 9.791470 9.998730 14.983100 14.560200
a0_min a0_flood Y1_intercept Y2_intercept Y3_intercept Y4_intercept Y5_intercept
St.Dev. 4.39786 4.72929 0.139538 2.09975 2.12893 2.92228 3.02605
MaxPost 118.98500 33.23810 0.334454 9.79147 9.99873 14.98310 14.56020

Estimation of the friction coefficients

In the main channel:

Estimation of the friction coefficients

In the floodplain:

Residuals

in terms of WSE

In terms of discharge

Notes:

  • High negative corelation between a0_kmin and a0_kmoy. They can be interchangeable and the result will be the same with a weighting or factor to compensate.

Bibliography:

PROUST, SEBASTIEN, and VLADIMIR I. NIKORA. 2025. “Dataset of a Laboratory Study on Flows in a Compound Open Channel with Transverse Currents.” Recherche Data Gouv. https://doi.org/10.57745/HJKRYH.
Proust, Sébastien, and Vladimir I. Nikora. 2020. “Compound Open-Channel Flows: Effects of Transverse Currents on the Flow Structure.” Journal of Fluid Mechanics 885 (February): A24. https://doi.org/10.1017/jfm.2019.973.